1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tom [10]
2 years ago
14

A certain industrial process yields a large number of steel cylinder whose lengths are distributed normally with mean 3.25 inche

s and standard deviation 0.05 inches. If two such cylinders are chosen at random and placed end to end what is the probability that their combined length is less than 6.60 inches? (round answer to two decimals)
Mathematics
1 answer:
Taya2010 [7]2 years ago
3 0

Answer:

Y = X_1 + X_2

If we find the expected value of Y we got:

E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005

And the deviation Sd(Y) = \sqrt{0.005}=0.0707

So then our random variable Y have the following distribution:

Y \sim N (\mu =6,5 , \sigma = 0.0707)

And we want to find this probability:

P(Y

And we can use the z score formula given by:

z=\frac{y -\mu_y}{\sigma_y}

And if we use the z score formula we got:

P(Y

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

X \sim N(3.25,0.05)  

Where \mu=3.25 and \sigma=0.05

We slect two observations X_1, X_2

And let denote the combined lenght as:

Y = X_1 + X_2

If we find the expected value of Y we got:

E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005

And the deviation Sd(Y) = \sqrt{0.005}=0.0707

So then our random variable Y have the following distribution:

Y \sim N (\mu =6,5 , \sigma = 0.0707)

And we want to find this probability:

P(Y

And we can use the z score formula given by:

z=\frac{y -\mu_y}{\sigma_y}

And if we use the z score formula we got:

P(Y

You might be interested in
NEED ANSWERED ASAP WILL REWARD BRAINLIEST
Luda [366]

Answer:

The sum of the first 100 terms is 60400

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

- We will use method (1)

- From the table the terms of the sequence are:

 10 , 22 , 34 , 46 , 58 , 82 , 94 , ............., where 10 is the first term

∵ an = a1 + (n - 1) d ⇒ explicit formula

∵ a1 = 10 and a2 = 22

∵ d = a2 - a1

∴ d = 22 - 10 = 12

- The 100th term means the term of n = 100

∴ a100 = 10 + (100 - 1) 12

∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198

∴ The 100th term is 1198

- Lets find the sum of the first 100 terms of the sequence

∵ Sn = n/2[a1 + an]

∵ n = 100 , a = 10 , a100 = 1198

∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400

* The sum of the first 100 terms is 60400

7 0
2 years ago
In an 11 team soccer league, each team plays once what is the total amount of games played?
stich3 [128]

Answer:

22

Step-by-step explanation:

11 x 2 = 22

22 teams played

4 0
2 years ago
Which of the following is an arithmetic sequence?<br> 00.2.4.6.<br> 01.24.8.<br> 0 1.4.8. 13....
Ahat [919]

Answer:

(A.) 00,2,4,6

Step-by-step explanation:

00+2=2

2+2=4

2+4=6

Each number is added by the same number, 2, so this is the arithmetic sequence.

6 0
2 years ago
Which postulate or theorem could be used to prove triangleLMQ is congruent to triangleLNP
Cerrena [4.2K]
I believe the correct answer is B. :)
7 0
3 years ago
Read 2 more answers
How to do slope intercept form word form?
Artyom0805 [142]
You can divide. i believe
4 0
3 years ago
Other questions:
  • Round 34,576 to the nearest thousand
    14·1 answer
  • the most a bowling ball can weigh is 7,258 grams. what is the most it can weigh when measured in pounds? explains plz
    5·1 answer
  • Semicircles
    15·1 answer
  • What is answer 6x+7-5x=10
    7·2 answers
  • Sandwich sales for one week are $1,275.00 and 300 sandwiches are sold. How much did each sandwich sell for assuming each sold fo
    9·2 answers
  • A friend of yours in your intro stats class obtains permission to randomly sample the University student body to conduct a satis
    10·1 answer
  • There are 9 apples.there are 6 fewer apples than oranges.how oranges are there
    11·1 answer
  • Can someone help me!
    15·2 answers
  • 4x + 16/12 What is the value of x in the equation= x - 4?
    11·1 answer
  • Nachelle is 1.45 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 23.05 meters. She stands 18.9 meters
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!